Solve for $x$ and $y$ using substitution. ${x+y = 6}$ ${x = 3y+2}$
Solution: Since $x$ has already been solved for, substitute $3y+2$ for $x$ in the first equation. ${(3y+2)}{+ y = 6}$ Simplify and solve for $y$ $3y+2 + y = 6$ $4y+2 = 6$ $4y+2{-2} = 6{-2}$ $4y = 4$ $\dfrac{4y}{{4}} = \dfrac{4}{{4}}$ ${y = 1}$ Now that you know ${y = 1}$ , plug it back into $\thinspace {x = 3y+2}\thinspace$ to find $x$ ${x = 3}{(1)}{ + 2}$ $x = 3 + 2$ ${x = 5}$ You can also plug ${y = 1}$ into $\thinspace {x+y = 6}\thinspace$ and get the same answer for $x$ : ${x + }{(1)}{= 6}$ ${x = 5}$